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AVprozaik [17]
2 years ago
15

Lisa's test grades are 79, 89, and 90. there will be one more test this year. if lisa wants her test average to be at least 88,

what is the lowest grade she can get on her last test?
Mathematics
1 answer:
erik [133]2 years ago
5 0
For this case, what we are going to do first is to assume that all the exams are worth the same percentage of the final grade.
 We have then that Lisa's average grade point equation is:
 88 =  \frac{79 + 89 + 90 + x}{4}
 Where,
 x: minimum note that lisa must obtain in the last exam.
 Clearing x we have:
 x = (88 * 4) - (79 + 89 + 90)

x = 94
 Answer:
 
the lowest grade she can get on her last test is:
 
x = 94
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If θ=0rad at t=0s, what is the blade's angular position at t=20s
babunello [35]
The attached figure represents the relation between ω (rpm) and t (seconds)
To find the blade's angular position in radians ⇒ ω will be converted from (rpm) to (rad/s)
              ω = 250 (rpm) = 250 * (2π/60) = (25/3)π    rad/s
              ω = 100 (rpm) = 100 * (2π/60) = (10/3)π    rad/s

and from the figure it is clear that the operation is at constant speed but with variable levels
            ⇒   ω = dθ/dt   ⇒   dθ = ω dt

            ∴    θ = ∫₀²⁰  ω dt  
 
while ω is not fixed from (t = 0) to (t =20)
the integral will divided to 3 integrals as follow;
       ω = 0                                          from t = 0  to t = 5
       ω = 250 (rpm) = (25/3)π            from t = 5   to t = 15
       ω = 100 (rpm) = (10/3)π            from t = 15 to t = 20

∴ θ = ∫₀⁵  (0) dt   + ∫₅¹⁵  (25/3)π dt + ∫₁₅²⁰  (10/3)π dt
     
the first integral = 0
the second integral = (25/3)π t = (25/3)π (15-5) = (250/3)π
the third integral = (10/3)π t = (25/3)π (20-15) = (50/3)π

∴ θ = 0 + (250/3)π + (50/3)π = 100 π

while the complete revolution = 2π
so instantaneously at t = 20
∴ θ = 100 π - 50 * 2 π = 0 rad

Which mean:
the blade will be at zero position making no of revolution = (100π)/(2π) = 50
















3 0
2 years ago
According to a 2014 research study of national student engagement in the U.S., the average college student spends 17 hours per w
Nadusha1986 [10]

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 17

For the alternative hypothesis,

µ < 17

This is a left tailed test.

Since the population standard deviation is not given, the distribution is a student's t.

Since n = 80,

Degrees of freedom, df = n - 1 = 80 - 1 = 79

t = (x - µ)/(s/√n)

Where

x = sample mean = 15.6

µ = population mean = 17

s = samples standard deviation = 4.5

t = (15.6 - 17)/(4.5/√80) = - 2.78

We would determine the p value using the t test calculator. It becomes

p = 0.0034

Since alpha, 0.05 > than the p value, 0.0043, then we would reject the null hypothesis.

The data supports the professor’s claim. The average number of hours per week spent studying for students at her college is less than 17 hours per week.

4 0
2 years ago
A teacher gives a test to a large group of students. The results are closely approximated by a normal curve. The mean is 74​, wi
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Answer:

Step-by-step explanation:

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Z score for 92nd percentile = 1.405

X score = 74+8(1.405) = 85.24

--------------------

B cut off is to next 16%

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Your cousin borrows $1125 to repair her car. The simple annual interest rate is 10%. She makes equal monthly payments of $25. Ho
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Answer:

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Step-by-step explanation:

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Answer:

Z = 8 + 2x2 + 2y2

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14 = 8 + 2r2

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